Electrically driven piezoelectric acoustic resonators have utility in a wide range of radio frequency applications. Piezoelectric acoustic resonators comprise a layer of piezoelectric material that has a thickness of 1/2 the acoustic wavelength at resonant frequency. Drive electrodes are formed on the top and bottom surfaces of the piezoelectric layer. A discrete piezoelectric resonator may be used, for example, as a frequency reference in an oscillator circuit. Several resonators can be combined in a ladder network to form a band pass filter.
For resonators, an important figure of merit is the quality factor (Q), defined as: ##EQU1## where f.sub.0 is the center frequency and .DELTA.f is the frequency width of the resonance. For a parallel plate resonator, ##EQU2## where Q.sub.m is the inherent Q of the resonator material, and R.sub.1 and R.sub.2 are the reflectivities of the two surfaces. For a free air (or vacuum) interface, the reflectivity R is very nearly 1. Thus, a piezoelectric thin film resonator can have a very high Q when freely suspended in air. Such resonators have been demonstrated in discrete form and as integrated filters.
Thin film resonators, however, are difficult to fabricate, very sensitive to stress, and very fragile. An alternative is to fabricate thin film resonators on solid supporting substrates. In this case, R.sub.1 is essentially 1 for the top interface with air, but R.sub.2 is determined by the acoustic impedance mismatch between the resonator material and the supporting substrate as follows: ##EQU3## and where .rho. is the material density and C is the acoustic velocity in the material. The larger the mismatch in acoustic impedance between the resonator material and supporting substrate, the larger the reflection. Unfortunately, the range of acoustic impedance values in available materials is not large enough to yield a very high Q for a single interface. However, if a sequence of layers of alternating high and low impedance materials is used, with each layer having a thickness of 1/4 acoustic wavelength at the resonant frequency, the reflections from each pair of layers (high and low impedance material) combine in phase at the resonant frequency. For normal incidence, the one-dimensional case yields a total reflectivity of EQU R'=1-(1-R).sup.N,
where
R' is the reflectivity of each pair of layers and N is the number of pairs. Thus, the Q of a resonator mounted on such a resonant acoustic isolator can be expressed as ##EQU4##
If the material losses are low, nearly arbitrary reflectivity can be achieved by using a sufficiently large number of layers. However, to minimize the number of pairs of layers required, one should choose materials with a large acoustic mismatch. For ease in fabricating a thin film piezoelectric resonator (including top and bottom electrodes) directly on the supporting layers of the acoustic isolator, it is highly desirable that reflector materials comprise electrical insulators. Thus, devices can be isolated by patterning the drive electrodes without the necessity of patterning the supporting layers of the acoustic isolator.
Silicon dioxide (SiO.sub.2) can be effective as the low impedance layer (Z.sub.a .apprxeq.13) in a resonant acoustic isolator because it is a low loss material, it can be deposited by a variety of techniques, and it is ubiquitous in the semiconductor world. There is a need, however, for a high acoustic impedance material that can be readily deposited using a technique compatible with SiO.sub.2 deposition to form a multilayer resonant acoustic isolator.